perhaps I should tell a little bit more about the motivation for my axioms:

?Axiom 1: Statements A are entities independent of layers, but get a truth value only in connection with a layer t,refered to as W(A,t).?

My introduction of layers to logic was a little bit similar to Max Planck introducing quants in physics:Not very plausible and I do not really like it, but it seems to work ?

With the layers, a liar statement was easier to handle:

If we define statement L by the following: For all layers t: W(L,t+1) := W (W(L,t) = -w ,1) ?The value of thus statement L is true (in layer t+1) iff the value of L is not true (in layer t?With the (universal) start W(L,0) = u we get: W(L,1) = -w, W(L,2) = w, W(L,3) = w, W(L,4) = w, ?So L , which is similar to the liar statement, is a statement with alternating truth values and this is allowed and no problem in layer theory thanks to the layers.

The next very special axioms are the axioms about meta statements:

?Axiom 5: (Meta-)statements M about a layer t are constant = w or = -w for all layers d >= 1. For example M := ´W(-w,3)= -w´, then w=W(M,1)=W(M,2)=W(M,3)=...(Meta statements are similar to classic statements)

For the motivation of these axioms, we have a look at axiom 1:There we find formulations like ?for all layers t?, so axiom 1 is a statement about all layers.As there is a hierarchy of layers and we are only allowed to use smaller layers for defining a truth value of a statement in a certain layer t0 (I have not formalized this completely yet) the axiom 1 can not belong to a certain layer t1.

On the other side I did not want to have infinite ordinal numbers in my layers,so I made statements about one ore more layers independent of layers by defining axiom 5.(I am not sure, if axiom 6 is needed at all, as layers are always in connection with truth values up to now.)

I do not know if we have to define (and with what more details), that all statements A need a definition of the form:?For all layers t: W(A, t+1) = ?? and on the right sides only statements of layers smaller than t+1 or meta statements are allowed.